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We propose a method for defining, identifying, and estimating the marginal treatment effect (MTE) without imposing the instrumental variable (IV) assumptions of independence, exclusion, and separability (or monotonicity). Under a new definition of the MTE based on reduced-form treatment error that is statistically independent of the covariates, we find that the relationship between the MTE and standard treatment parameters holds in the absence of IVs. We provide a set of sufficient conditions ensuring the identification of the defined MTE in an environment of essential heterogeneity. The key conditions include a linear restriction on potential outcome regression functions, a nonlinear restriction on the propensity score, and a conditional mean independence restriction that will lead to additive separability. We prove this identification using the notion of semiparametric identification based on functional form. And we provide an empirical application for the Head Start program to illustrate the usefulness of the proposed method in analyzing heterogenous causal effects when IVs are elusive., Comment: 41 pages, 6 figures, 2 tables

Functional magnetic resonance imaging (fMRI) plays a crucial role in neuroimaging, enabling the exploration of brain activity through complex-valued signals. These signals, composed of magnitude and phase, offer a rich source of information for understanding brain functions. Traditional fMRI analyses have largely focused on magnitude information, often overlooking the potential insights offered by phase data. In this paper, we propose a novel fully Bayesian model designed for analyzing single-subject complex-valued fMRI (cv-fMRI) data. Our model, which we refer to as the CV-M&P model, is distinctive in its comprehensive utilization of both magnitude and phase information in fMRI signals, allowing for independent prediction of different types of activation maps. We incorporate Gaussian Markov random fields (GMRFs) to capture spatial correlations within the data, and employ image partitioning and parallel computation to enhance computational efficiency. Our model is rigorously tested through simulation studies, and then applied to a real dataset from a unilateral finger-tapping experiment. The results demonstrate the model's effectiveness in accurately identifying brain regions activated in response to specific tasks, distinguishing between magnitude and phase activation.

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be computationally efficient via image partitioning and parallel computation while being competitive with state-of-the-art methods. We support these claims with both simulated numerical studies and an application to real cv-fMRI data obtained from a finger-tapping experiment.

Background:Diverse tacrolimus population pharmacokinetic models in adult liver transplant recipients have been established to describe the PK characteristics of tacrolimus in the last two decades. However, their extrapolated predictive performance remains unclear.Therefore,in this study,we aimed to evaluate their external predictability and identify their potential influencing factors. Methods:The external predictability of each selected popPK model was evaluated using an independent dataset of 84 patients with 572 trough concentrations prospectively collected from Huashan Hospital. Prediction and simulation based diagnostics and Bayesian forecasting were conducted to evaluate model predictability. Furthermore, the effect of model structure on the predictive performance was investigated.Results:Sixteen published popPK models were assessed. In prediction-based diagnostics,the prediction error within 30% was below 50% in all the published models. The simulation based normalised prediction distribution error test and visual predictive check indicated large discrepancies between the observations and simulations in most of the models. Bayesian forecasting showed improvement in model predictability with two to three prior observations. Additionally, the predictive performance of the nonlinear Michaelis Menten model was superior to that of linear compartment models,indicating the underlying nonlinear kinetics of tacrolimus in liver transplant recipients.Conclusions:The published models performed inadequately in prediction and simulation based diagnostics. Bayesian forecasting may improve the predictive performance of the models. Furthermore, nonlinear kinetics of tacrolimus may be mainly caused by the properties of the drug itself, and incorporating nonlinear kinetics may be considered to improve model predictability.